arXiv subjects

Long Teng

Publications and source records attributed to Long Teng.

20 records · Page 2Linked to original sources

arXiv2019

A Review of Tree-based Approaches to solve Forward-Backward Stochastic Differential Equations

In this work, we study solving (decoupled) forward-backward stochastic differential equations (FBSDEs) numerically using the regression trees. Based on the general theta-discretization for the time-integrands, we show how to efficiently use regression tree-based methods to solve the resulting conditional expectations. Several numerical experiments including high-dimensional problems are provided to demonstrate the accuracy and performance of the tree-based approach. For the applicability of FBSDEs in financial problems, we apply our tree-based approach to the Heston stochastic volatility model, the high-dimensional pricing problems of a Rainbow option and an European financial derivative with different interest rates for borrowing and lending.

math.NA↗

arXiv2018

A Multi-step Scheme based on Cubic Spline for solving Backward Stochastic Differential Equations

In this work we study a multi-step scheme on time-space grids proposed by W. Zhao et al. [28] for solving backward stochastic differential equations, where Lagrange interpolating polynomials are used to approximate the time-integrands with given values of these integrands at chosen multiple time levels. For a better stability and the admission of more time levels we investigate the application of spline instead of Lagrange interpolating polynomials to approximate the time-integrands. The resulting scheme is a semi-discretization in the time direction involving conditional expectations, which can be numerically solved by using the Gaussian quadrature rules and polynomial interpolations on the spatial grids. Several numerical examples including applications in finance are presented to demonstrate the high accuracy and stability of our new multi-step scheme.

math.NA↗